Acute anxiety during the COVID-19 pandemic was associated with higher levels of everyday altruism

Prior laboratory research has suggested that humans may become more prosocial in stressful or threatening situations, but it is unknown whether the link between prosociality and defense generalizes to real-life. Here, we examined the association between defensive responses to a real-world threat (the COVID-19 pandemic) and everyday altruism. Four independent samples of 150 (N = 600) US residents were recruited online at 4 different timepoints, and self-report measures of perceived COVID-19 threat, defensive emotions (e.g., stress and anxiety), and everyday altruism were collected. Our operationalization of defensive emotions was inspired by the threat imminence framework, an ecological model of how humans and animals respond to varying levels of threat. We found that perceived COVID-19 threat was associated with higher levels of everyday altruism (assessed by the Self-report Altruism scale). Importantly, there was a robust association between experiencing acute anxiety and high physiological arousal during the pandemic (responses typically characteristic of higher perceived threat imminence), and propensity to engage in everyday altruism. Non-significant or negative associations were found with less acute defensive responses like stress. These findings support a real-life relation between defensive and altruistic motivation in humans, which may be modulated by perceived threat imminence.

Model 1 -Perceived COVID-19 threat, stress, anxiety and depression The full model contained the 4 main predictors of interest (fixed effects), plus a random intercept and random slope for each predictor nested by Week. Initially, we wanted to model random intercepts and random slopes by State as well, but because we had limited data nested per state, we decided the model did not have enough information per State to estimate these parameters. For instance, we would require 230 random effects estimates if we included State as a random effect in the model. Additionally, the random effects estimates for State can hardly model any additional random variance at all. As an example, the random effects coefficients for the 46 intercepts predicted for each state were all zero. The estimated intercept for each week is non-zero. We therefore decided to remove State as a random effect and only included Week. It should be noted that none of the results of the model actually change if State is included. However, given the lack of variance the random effect of State contributed to the model, we believe its removal is justifiable.
We used the R package lme4 to model everyday altruism (Self-Report Altruism scale, SRA in the code) as a function of: Perceived COVID19 threat (risk perception, RP in the code), Stress (perceived stress scale, PSS in the code), Anxiety, and Depression. Additionally, we modelled random intercept and random slope estimates per Week for each of the 4 predictors. m1 <lmer(SRAz~RPz + PSSz + Anxietyz + Depressionz +  Perceived Covid19 threat and Anxiety were both statistically significant predictors of SRA. Note that this model (and the subsequent models below) gave us a warning stating we had a boundary (singular) fit. These warnings indicate that one or more variance estimates are very close to zero. While random effects could be removed to eliminate this warning, we felt the inclusion of all random effects was important. Because our models account for a large amount random variance (intercepts and slopes) associated with each week, our model also generalises better to other weeks and individuals (Yarkoni, 2019). While additional random effects can reduce power, they can also reduces the Type-I error rate. Given that with enough data every difference will be statistically significant (Meehl, 1967), and given our sample size, we felt this was a reasonable compromise.
Model 2 -adding gender, age, employment, socio-economic status We also wanted to see how additional fixed effects, not related to our main predictions, explained everyday altruism. To minimize convergence problems, we first selected additional predictors with potential associations with our dependent variable (everyday altruism) and selectively added them to the model (see below). We therefore ran a new model with 4 additional predictors: Age, Gender, Employment, and socioeconomic level. Our goal was to identify predictors associated with SRA at our pre-defined threshold (p < 0.05) so that we could add them to the final model.  This model, however, did not converge. Convergence issues can be caused by a number of factors, and we decided to explore ways to get this model working properly.
In an attempt to correct convergence issues, we centered age in the model (it was the only variable that could be centered). This can sometimes help when a model does not converge, and is a common strategy when first attempting to deal with non-convergence. The model now converges, and we can see that age is the only clear significant predictor of SRA. However, employment appeared to be a potentially relevant predictor (marginally significant association with SRA), so we included it in the final model.

Model 3 -Adding Age and Employment to Model 1
We added age and employment to the initial model. However, the updated model no longer converged. Another common strategy to aid convergence is to remove the most complex random effects (i.e. random slopes) iteratively from the model. Because the random effects of age accounted for the least amount of variance in the new model, we removed the random slope estimate of age and re-ran the model.  The full model failed to converge, but the results were in the same direction as with the other models.

Testing assumptions
1. Homoskedasticity: Residuals are randomly distributed around the regression line. 2. Normality: residuals are normally distributed as can be assessed using either a histogram or qq-plot. 3. Random effects residuals: The random effects estimates should also be normally distributed around zero

Modelling everyday altruism within each
week We tested our model in each independent week to examined whether the observed associations between self-reported altruism, and perceived covid-19 risk and anxiety held over time (rather than accounting for that by modelling week as a random effect, as done in the previous analysis).
When modelling each week separately, the model used above had to be simplified to provide reliable estimates and avoid convergence issues, given the reduction in the number of observations (600 to 150 participants). Specifically, we removed all random effects of by all fixed effects, because we were no longer using Week as random effect (SRAz~RPz + Anxietyz + Depressionz+ PSSz + agez + Employment). Results (Table 3) show anxiety was consistently associated with increased everyday altruism within each week.

State variation in altruism and COVID-19 risk perception
Our main analysis using accounted for variation introduced by variability between weeks of data collection. Presumably, there could be variability associated with each location we collected data from, even if this variability was not enough to influence the inclusion of state into our model. However, we understand state variation could be of interest to some readers. We thus include here some exploratory plots to help readers visualise our data in reference to the state.
The first plot presented illustrates the number of cases per State in the 4 weeks of data collection.  One question we can anticipate from readers is that, due to the great variability in severity of the pandemic in different states (e.g., NY versus Alaska), it may be that the key experimental effects could vary greatly between states. However, as explained above, most states in our sample had a reduced number of cases, making variation due to State a likely noisy effect. For descriptive purposes, here we selected states that we collected 20 or more observations from. Below, we plot results from those states for variables of interest in our study, namely Perceived Covid19 threat (RP), Self-Reported Altruism, and Total Confirmed COVID cases.

Week
Week The plot above depicts how Perceived Covid19 threat, self-reported altruism and Number of confirmed cases evolved over 4 weeks of data collection, for each of the states with N>20. As can be seen in the plot, NJ and NY were the States that had the largest and most obvious increase in number of cases. For Perceived COVID19 threat and self-reported altruism, no week-related pattern seems to emerge across all the states included. We next plotted Perceived Covid19 threat and Self-Reported Altruism from those 2 States below, to illustrate that even in States with a clear rise in cases, these measures do not seem to meaningfully change over the 4 weeks. Week 1 Week 2 Week 3 Week 4 Week Everyday altruism (SRA) The ANOVAs below show no significant changes in Perceived COVID-19 threat in NY/NJ over the 4 weeks. For SRA, there is an apparent decrease from week 1 to week 2, but consistent pattern emerged. Note that this analysis is purely exploratory, as the sample size per week is very small (week 1: n=19, week 2: n = 12, week 3: n=10; week 4: n = 20).

Simulation-based power analysis for random effects model
Because our study was constrained by time and resources, we did not conduct a formal power analysis prior to data collection and analysis. Power analyses can still be useful after a study is completed as they can reveal how much power a study theoretically had to detect a range of effect sizes of interest. We opted to model a simple power function at fixed (i.e. discrete steps) effect sizes for the 4 key predictors (Perceived Covid-19 Threat, RP; Anxiety; Stress, PSS; Depression) in our model by simulating a dataset. We first simulated standardised questionnaire data to match how it might reasonably be generated from individuals randomly sampled from the population. Thus, we simulated data with 600 observations for 4 parameter by drawing values randomly from a normal distribution with a mean of zero, standard deviation of 1, and a correlation between each observations parameter estimate of 0.4. Additionally, each observation was assigned a week, and a random variance component was included with each observation by drawing 4 values from a normal distribution with a mean of zero and a standard deviation of 1. We caculated an SRA score for each observation in the model by multiplying a fixed parameter estimate to each simulated questionnaire score and then adding together the linear combination of these values (along with weekly random variance and a randomly drawn error term). The data structure for the first 5 simulated observations (i.e. participants) can be seen below.

Fitting the model
The simulated data were fit to the same model used in the study. We fixed all slopes at 0.3 in the simulation, and thus, we expected their subsequent random effects model estimates to roughly match the fixed 0.3 terms. As can be seen below, these assumptions are roughly met in our model output.

Running the power simulations
To assess how much power our study had to detect different effect sizes of interest, we ran a power simulation. Here we asked how much power we would have to detect a wide range of effect sizes for each parameter in our model. We thus simulated "power" for 9 effect sizes (0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) for each of the 4 parameters. Each simulation started by first simulating new SRA values based on the current fixed effect size, refitting the model to the new simulated SRA values, and running the statistical model again. This was repeated 1000 times for each effect size and each parameter for a total of 36000 simulation.

Power curve
Plotted below are approximated power curves, each showing the proportion of simulations that gave a significant result for each parameter at each fixed effect size. Because power is a contiuous function, rather than a single value, the plot can be analysed to assess how much power the current study would have to detect each effect size, conditional on our random effects model. Each colored line in each plot represents the estimated power for 1 predictor at each fixed effect size, with grey lines showing the other power curves of the other predictors to allow quick comparisons. As an example of how to interpret the graph below, the power simulation indicates that the sampling procedure for the current study has between 88% and 94% power to detect a 0.3 effect size for each parameter. This logic can be extended to any other fixed effect sizes.

Perceived Covid−19 Threat (RP)
Stress (    Removing depression from the full model also did not change the significance of the anxiety coefficient, and again made the PSS coefficient statistically significant in the negative direction. Note: Say something about how PSS and anxiety have opposing effects on altruism, and that it is improtant to keep Depression in the model because it and PSS are correlated.

Addressing model singularity (revisions August 2022)
To address the singular fit in our main models, we sequentially removed random effects until the model was no longer singular. The ?isSingular command in lmer explains that there is no consensus on how best to deal with singularity, but provides a number of empirically justified ways to deal with it. We opted for Barr et al.'s (2013) "keep it maximal" approach. We considered the model in its current singular state to be our maximal model (random slopes for all coefficients and a random intercept) and began taking random effects out until it was no longer singular. This resulted in a model with only random intercept per week.